Compositionality and Reachability with Conditions on Path Lengths

In model-checking the systems under investigation often arise in the form of products. The compositional method, developed by Feferman and Vaught in 1959, fits to this situation and can be used to deduce the truth of a formula in the product from information in the factors. Building on earlier work of Wöhrle and Thomas (2004), we study first-order logic with reachability predicates over finitely synchronized products (i.e. synchronized products with a finite number of synchronization transitions). We extend the reachability predicates by conditions on the length of the corresponding paths, formulated in Presburger arithmetic. For finitely synchronized products with these enhanced reachability predicates we prove a composition theorem and then show that severe limitations exist for generalisations of this result.